British Prime Minister Theresa May and European Commission President Jean-Claude Juncker. [Photo/Agencies]

British Prime Minister Theresa May and European Commission President Jean-Claude Juncker met in Brussels on Wednesday evening for crucial Brexit talks aimed at detailing the future relationship between the United Kingdom and European Union.

The sit down was a prequel to a special EU summit on Sunday at which European leaders are expected to agree the final text of the 585-page Brexit withdrawal deal that May presented to her cabinet and the British Parliament last week.

Hardline Brexiteers who wanted a cleaner break from Europe disliked the 39-billion-pound ($50-billion) provisional deal and some members of Parliament from May's ruling Conservative Party began a process to unseat her as leader but that attempt looks to have run out of steam.

Britain and the other 27 members of the EU are also working on a political statement to accompany the withdrawal agreement that sets out a general vision of how they should interact in future.

Crucially, May plans to meet EU officials before Sunday to explore "technological" solutions that might allow a soft border in Ireland, instead of the contentious "backstop" plan currently in the draft Brexit withdrawal deal.

The so-called backstop is a last-resort to keep an open border on the island of Ireland in the event of the UK leaving the EU without a trade deal but it is controversial because critics say it could tie the UK to EU rules indefinitely.

The backstop provision has been the main source of opposition in the UK to the draft withdrawal deal. The deal, if rubber-stamped on Sunday, will be debated and voted on in the British Parliament.

The Sun newspaper has reported that senior members of May's government have warned her she faces having the deal voted down in Parliament if she fails to win concessions from Juncker.

While the draft Brexit withdrawal deal has been criticized by some Conservative MPs, and two Cabinet ministers resigned over it, May looks to have avoided a revolt.

One of her main critics, backbench MP Jacob Rees-Mogg, looked desperate on Tuesday when he conceded too few letters had been sent to party officials to trigger a leadership vote.

And cabinet minister Amber Rudd said on Wednesday on BBC Radio 4's Today program that Parliament has no stomach to leave the EU without a deal.

"It's my view that Parliament, the House of Commons, will stop no-deal," she said. "There isn't a majority in the House of Commons for that to take place."

The prime minister has repeatedly said the choice is between her deal and no-deal.

A YouGov survey commissioned by the Times newspaper says 46 percent of voters believe May will keep her job, compared to 33 percent a week ago.